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Article Dans Une Revue Inverse Problems Année : 2018

A time reversal algorithm in acoustic media with Dirac measure approximations

Carine Lucas
Yannick Privat

Résumé

This article is devoted to the study of a photoacoustic tomography model, where one is led to consider the solution of the acoustic wave equation with a source term writing as a separated variables function in time and space, whose temporal component is in some sense close to the derivative of the Dirac distribution at t  =  0. This models a continuous wave laser illumination performed during a short interval of time. We introduce an algorithm for reconstructing the space component of the source term from the measure of the solution recorded by sensors during a time T all along the boundary of a connected bounded domain. It is based at the same time on the introduction of an auxiliary equivalent Cauchy problem allowing to derive explicit reconstruction formula and then to use of a deconvolution procedure. Numerical simulations illustrate our approach. Finally, this algorithm is also extended to elasticity wave systems.

Dates et versions

hal-01866862 , version 1 (03-09-2018)

Identifiants

Citer

Elie Bretin, Carine Lucas, Yannick Privat. A time reversal algorithm in acoustic media with Dirac measure approximations. Inverse Problems, 2018, 34 (4), ⟨10.1088/1361-6420/aaaca9⟩. ⟨hal-01866862⟩

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